Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Let ABC be the triangle and D be the mid-point of AB and DE || BC. By theorem 6.1, If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, the other two sides are divided in the same ratio. So, In △ ABC, Since, AE = EC. ∴ E bisects AC. Hence, proved that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

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In figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

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Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

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Mathematics

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Triangles

Related Questions

In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

In figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.